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Title: Replies to Referee Re GRAVITY

Descriptive symbol: UDT - Unspecified Document Type

Category of document: Scientific Papers

Sub-Category of document: Scientific Correspondence


« Gravityreply 8.29.98 » (last modified on Saturday, August 29, 1998; 9 :15 PM)
« Gravity, ref2, 8.28.98 » (last modified on Saturday, August 29, 1998; 10 :51PM)

(A.D. 01-12-25) 


Reviewer’s words in quotes: “...”; reply in brackets” [...].

“The author is a well-known expert on the mathematics of quantum field theory but I am not at all happy with his attempt to provide an alternative gravitational theory to that of Einstein, as presented in this paper.”

[It is to be expected that a professional proponent of General Relativity will be disappointed by the emergence of an alternative theory, but such disappointment is obviosuly neither here nor there scienficially. The scientific question is only whether the alternative theory does the job empirically and is consistent with fundamental scientific principles outside the realm of gravitation.]

“It does not appear that the author has faced up to the reasons for the light-cone structure of spacetime being different from that of flat space or of Einstein’s static spherical universe. In such a conformally flat spacetime, if light rays follow along the light cones, then there would be no light deflection by a massive body.”

[Virtually all large-scale physical theories make a distinction between the large-scale properties of the space-time arena on the one hand, and local interaction effects. Such local effects, from the interaction of electromagnetic with gravitational fields, to the local interactions of elementary particles in general, are modelled separately from the large-scale geometry. The reviewer’s objection to the Einstein universe would apply equally to Einstein’s 1917 paper modelling large scale gravitation, and it is obvious that there Einstein contemplated no exclusion of local graviational or other local interactive effects. The Einstein model was later extolled by one of the great authorities on GR, C. Moller, in his classic book on GR, as an apparently excellent description of the the large-scale gravitational structure of the universe.

There is no contradiction whatsoever, according to this very generally recognized procedure, between a large-scale Minkowski space or Einstein universe, and the bending of light. It is only in GR that light rays invariably follow a geodesic according to some metric. Indeed, Einstein himself, in the very first paper on his Equivalence Principle in 1907, noted that it implies the generic bending of light in a gravitational field, writing: ‘From this [i.e. the Equivalence Principle-my interpolation] it follows that those light rays that do not propagate along the xi-axis are bent by the gravitational field...’. 

“There is now a great deal of observation (sic) support for such light deflection. In fact, the subject of gravitational lensing depends fundamentally on this phenomenon, this being now an extremely active and well confirmed area of observational cosmology. If one is not to violate local causality, the only way in which light could fail to follow the light cones would be if they are slowed down (rather than speeded up) by some effective refractive index.”

[As noted in our previous comment, light deflection has been understood to be implied by the Equivalence Principle virtually since Special Relativity was first proposed. A rigorous and clear detailed derivation for the classical case of light passing close to the sun is given in the well-known paper by disinguished physicist L. I. Schiff, ‘On Experimental Tests of the General Theory of Relativity”, in Am. J. Phys. 28 (1960),340-343. The Einstein Equivalence Principle is incorporated in our alternative theory in the stronger form of global conformal invariance of fundamental physical interactions (modulo, of course, the actual state of the Universe). It is thus not at all the case that light could be deflected only if it follows the geodesics relative to a curved metric, or encounters a nontrivial refractive index.]

“Such behaviour would be in violation of the confirmed type of light bending that occurs in the Schwarzschild spacetime.”

[The reference to the Schwarzschild spacetime, which exists only as a theoretical construct in GR, is a clear demonstration of the implicit circularity in the reviewer’s argument against our alternative theory. In effect, it is assumed that GR is right, and hence the alternative can not be.]

“The author claims (on p.17) that 2 of the 3 original tests (including light deflection) follow from the equivalence principle. However, this is not correct, as there is no delfection in the Nordstrom theory, which satisfies the equivalence principle. Like the author’s theory Nordstrom’s theory uses a conformally flat metric for which light deflection does not occur.”

[As noted above, from Einstein in 1907 to Schiff in 1960, and beyond, it has always been clear that light deflection follows from the Einstein Equivalence Principle. The Nordstrom theory appears consistent with the equality of inertial and gravitational mass, but that is not relevant to photons, and makes no essential use of the full principle, which Einstein stated in its most explict and mature form, in ‘Uber Friedrich Kottlers Abhandlung “Uber Einstein’s
Aequivalenz hypothese und die Gravitation”, Ann. Physik 51 (1916) ’ as follows:

Principle of Equivalence. Starting from this limiting case of the special theory of relativity, one can ask oneself whether an observer, uniformly accelerated relative to K in the region considered, must understand his condition as accelerated, or whether there remains a point of view for him, in accordance with the (approximately) known laws of nature, by which he can interpret his condition as “rest”. Expressed more precisely: do the laws of nature, known to a certain approximation, allow us to consider a reference system K’ as at rest, if it is accelerated uniformly with respect to K? Or somewhat more generally: Can the principle of relativity be extended also to refence systems, which are (uniformly) accelerated relative to one another. The answer runs: As far as we really know the laws of nature, nothing stops us from considering the system K’ as at rest, if we assume the presence of a gravitational field (homogeneous in the first approximation) relative to K’; for all bodies fall with the same acceleration independent of their physical nature in a homogeneous gravitational field as well as with respect to our system K’. The assumption that one may treat K’ as at rest in all strictness without any laws of nature not being fulfilled with respect to K’, I call the “principle of equivalence”. 

The infinitesimal transformation from the inertial frame at K to that at K’ is an infinitesimal acceleration, or as shown by Hill and predecessors, an infinitesimal conformal (i.e. SU(2,2)) transformation, while conversely any infinitesimal conformal transformation is built up group-theoretically from infinitesimal (and therefore uniform) accelerations. Thus the EEP may quite directly be interpreted as infinitesimal conformal invariance of the fundamental forces and interactions of nature, and as such forms the basis for the chronometric theory, which exponentiates local to global conformal invariance. Nordstrom’s theory does not incorporate EEP in this strong form, from which time and space dilation and contraction effects result, as already made explicit in Einstein’s 1907 paper, and which form the basis of Schiff’s presentation of the deflection of light from the EEP. 

“I believe that there is some confusion in the author’s mind (p.9) between the effects of conformal transformations (which comprise his SU(2,2) group) and the coordinate transformations that correspond to a uniform acceleration (the so-called “Rindler coordinates”). Whereas straight worldlines are transformed to curves of uniform acceleration by SU(2,2) transformations, this is really quite a different thing from choosing a uniformly accelerating frame (as Rindler achieves).”
[ The reviewer does not appear to appreciate the identity between the general group-theoretic issue in transformation to a uniformly moving coordinate system by a Lorentz transformation, and to a uniformly accelerated coordinate system by a conformal transformation. Local coordinates x are transformed in both cases by well-defined infinitesimal transformations. In the non-relativistic limit c -> ∞, an linfinitesimal Lorentz transformation converges to an infinitesimal Galilean transformation, validating its interpretation as a transformation to moving coordinates, e.g. as emphasized in the well-known paper on space and time by Minkowski in 1908. Totally analogously, In the non-relativistic limit, a infinitesimal special conformal transformation converges to a infinitesimal acceleration, as shown on page 9. The situation is clearcut and quite devoid of confusion.]

“The most serious objection that I have to this paper is that the author makes no real attempt to square his theory with the superbly precise confirmation of Einstein’s theory that is provided by the binary pulsary observations made by Taylor and Hulse. There is a brief reference to this work on p. 19 together with a statement that its analysis is “beyond the scope of this paper”. 

[Granted that the observations of Taylor and Hulse represent a successful monumental and important undertaking, the analysis of their data is another matter. The raw material represented by their highly extensive time of arrival observations are incapable of use for theoretical purposes until it has been extensively reduced. This reduction has up to now itself been based on GR, or procedures and concepts derived from GR, from the work of Blandford and Teukolsky, in Astrophys. J. 205 (1976) 580-591, onward. This is not to say that the results are incorrect, but only that there is a definite element of circularity that is involved in the claimed confirmation of GR by the Taylor-Hulse observations.
To reduce these observations alternatively in the framework of chronometric theory would e an enormous undertaking, paralleling one or two decades of research before definitive procedures were evolved by Taylor and Amour and others. The exposition of the chronometric gravity theory stands independently as an extremely natural interpretation, within the framework of modern mathematical physics, of the EEP, that is consistent with the classic empirical tests, and is eminently quantizable, relatively free of adjustable parameters, and specific. It thus appears appropriate and interesting to report on these aspects of the theory at this time, and open up the theory to general 

“The author tries to suggest that some of the mathematical estimates used in this work are not fully justified and he gives reference to some papers to support this contention.”

[There is no doubt whatsoever that GR does not include, either theoretically a priori or by virtue of later rigorous development, a mathematically well-defined treatment of the two-body problem; and that leading mathematical general relativists affirm this to be the case. Attempts made to make expansions of solutions of the field equations in inverse powers of c and correlate them with the two-body problem have never attained mathematical convergence. Since there is no well-defined underlying theory, it is impossible to estimate or make any rigorous statement as to the degree of approxmation to rigorous GR of the analytical procedures used in the putative confirmation of GR based on the reduced Taylor-Hulse data. This confirmation is in fact described by M. Walker and C. M. Will, among the general relativists most supportive of the analysis of the Taylor-Hulse data, as indicative rather than suggestive of convincing”, and use a heuristic argument involving various unsubstantiated assumptions, in Astrophys. J. Lett. 242, L129-L133 (1980). Later work, notably that of T. Damour, in part with Taylor, also exempify the sensitivity to higher order terms in 1/c, and the many assumptions, correctionsand procedures derived in part from GR considerations, involved in reducing the directly observed time of arrival data, e.g. in ’Binary pulsars as probes of relativistic gravity’, Phil. Trans. R. Soc. Lond. A341 (1992), 135-149.

“However, there is no doubt that authors of these references, subtleties aside, would agree that the Taylor-Hulse analysis gives clear support to Einstein’s theory.” 

[Neither J. Ehlers, the senior author of one such reference, or any other leading general relativist, has published a withdrawal of their reservations about the mathematical and theoretical basis of the adaptation to the two-body problem of GR in its fundamental form. To the extent that they may now be prepared to support this analysis, in view of its broadly accepted appearance as confirmation of GR, this can only be on a heuristic and practical level. Ehlers and other rigorous general relativists have long expressed the view that the absence of any fundamental two-body theory in GR is no mere ‘subtlety’, but a basic issue.]

“ In any case, whatever objections one might have to the details of this work, it is clear that the binary pulsar system does indeed emit energy in the form of gravitational waves.”

[This is not clear at all. It is only in the framework of GR and the assumed validity of the heuristic adaptation of the field equations to the two-body problem involved in the binary pulsar system that energy appears emitted by the system. There is no special reason why the same should not be true in chronometric theory, or why the effect could not equally be described as due to production of gravitational waves.]

“ The energy of these waves is fully accounted for in the standard Einstein theory and agrees with enormous precision with the observations.”

[The “enormous precision” is internal to the version of GR used in the analysis, rather than a matter of agreement of prediction with an independently directly observed quantity, as in the classical empirical tests. It is thus much more of a self-consistency check than than a direct empirical correlative. In addition, the so-called ‘standard Einstein theory’ is extremely flexible and non-uniquely defined, particular as regards the relevant issue of spatial asymptotics and incoming waves. Granted that the theoretical analysis gives consistent results, the ambiguity in the GR notion of energy inherently limits apparent energy conservation in the binary pulsar context to a result significantly dependent on the particular choice of the coordinates adopted for the analysis.]

“The author seems to be arguing that the lack of energy conservation is the serious flaw in Einstein’s theory that his own theory is needed in order to correct.”

[A number of flaws, hardly less serious than the lack of energy conservation, were cited in the article. In any even, it is generally granted, even by proponents of GR, that energy is not conserved in GR. For example, P.A.M. Dirac, a leading theoretical physicist and the author of a book of GR, has written in “Energy of the Gravitational Field”. Phys. Rev. Letters 2 (1959). p. 368:
‘Einstein’s equations for the gravitational field are valid for any system of coordinates and make it difficult for one to distinguish physical effects from effects of curvature of the coordinate system. In consequence there is no obvious definition for the energy of the gravitational field. The usual definition, in terms of a component too of the stress pseudotensor, makes the energy depend very much on the system of coordinates and is thus not satisfactory.’
A leading exponent of Big Bang cosmology, P.J.E. Peebles has written in Principles of Physical Cosmology, Princeton University Press 1993, p.139:
‘The resolution of this apparent paradox is that while energy conservation is a good local concept, as in equation (6.18), and can be defined more genreally in the special case of an isolated system in asyptotically flat space, there is not a general global energy conservation law in general relativity theory.’
Neither is there a tenable local energy conservation law, e.g. local energy conservation implies global energy conservation in a compact space, since such a space can be covered by a finite number of arbitrarily small local regions.

“The binary pulsar work is a clear indication that there is no such flaw in the Einstein theory, but energy conservation (in the form that we observe it) is one of general relativity’s great strengths”

[The last part of this statement appears to be entirely at variance with general opinion by experts on GR, such as those just cited. The binary pulsar analysis assumes local energy conservation, rather than establishes it. The self-consistency of the analysis and its consistency with the statistics of the reduced time of arrival data exemplies consistency with local energy conservation in terms of suitable coordinates adapted to the observational context, in the asymptotically flat context, rather than in general.